I hate to hear this Waggy, but it sounds like you got my neighbors next door now, LOL. The way I dealt with my screw loose neighbors was I proceeded to call the cops and code enforcement on every stupid thing they ever did after they started in on me for no reason right after I moved in. They finally got the message that I was not going to put up with their ridiculous shit, but it took a while. Now, we are at a quiet impasse, thankfully, and it helped that one of her thug sons moved out a few years ago. Now it's just her and one 18 year old son ATM. I am assembling the parts for a outside security system that I am going to install pretty soon, too. You can't let these imbecile thugs push you around, or they will continue to target you mercilessly when you least expect it, like working in your yard or going to or from your car.
I would have called the cops if her gang was trying to intimidate you into a fight. You need to get their obnoxious behavior documented by the cops every chance you get for your own safety. Show these morons no mercy. And guns are good for you, especially if they are threatening to use one on your pet. Threatening to use a firearm against you or your pet or your property is against the law, and is a terroristic threat of violence. Do NOT put up with this shit and keep turning the other cheek, or it WILL get out of your control. Good luck!